An angular analysis of Lambda(0)(b) -> J/psi Lambda decays is performed using a data sample corresponding to 1.0 fb(-1) collected in pp collisions at root s = 7 TeV with the LHCb detector at the LHC. A parity violating asymmetry parameter characterising the Lambda(0)(b) -> J/psi Lambda decay of 0.05 +/- 0.17 +/- 0.07 and a Lambda(0)(b) transverse production polarisation of 0.06 +/- 0.07 +/- 0.02 are measured, where the first uncertainty is statistical and the second systematic.